Given a "good" graph G (i.e., one for which all intersecting graph edges intersect in a single point and arise from four distinct graph vertices), the crossing number is the minimum possible number of crossings with which the graph can be drawn, including using curved (non-rectilinear) edges. Several notational conventions exist in the literature, with some of the more common being cr(G) (e.g., Pan and Richter 2007; Clancy et al. 2019), CR(G), cr_0(G) (e.g., Pach and Tóth 2005), and ν(G).

doublecross graph | Guy's conjecture | Klein bottle crossing number | planar straight line embedding | projective plane crossing number | rectilinear crossing number | singlecross graph | smallest cubic crossing number graph | straight line embedding | toroidal crossing number | Zarankiewicz's conjecture